Perhaps the showers contained different bays and they showered at the same time but in different bays.
That's "together" in one sense, but not "together."
“It’s a stretch to assume they showered “together.”
Not really. The norm for the workout clubs and the university field house where I worked until recently was a rectangular room with multiple shower heads and drains. The locker rooms consist of long rows of lockers with a wooden bench in front.